Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-2x-3y &= -8 \\ -8x+9y &= 4\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $3$ and the bottom equation by $1$ $\begin{align*}-6x-9y &= -24\\ -8x+9y &= 4\end{align*}$ Add the top and bottom equations. $-14x = -20$ Divide both sides by $-14$ and reduce as necessary. $x = \dfrac{10}{7}$ Substitute $\dfrac{10}{7}$ for $x$ in the top equation. $-2( \dfrac{10}{7})-3y = -8$ $-\dfrac{20}{7}-3y = -8$ $-3y = -\dfrac{36}{7}$ $y = \dfrac{12}{7}$ The solution is $\enspace x = \dfrac{10}{7}, \enspace y = \dfrac{12}{7}$.